A higher power could also be an omnipresent intelligence with no interest what so ever in human affairs.
In my opinion the whole debate should be using a terminology regarding spiritual awareness and not of religion since the latter is much more loaded with assumptions which biases the results. This way an atheist could actively be pursuing a personal spiritual program.
Are you saying that people who don't believe in advanced alien tech also do not believe in God? Or am I having a mental breakdown? I'm fairly sure I know what a subset is and its logical implications.
To go from there to ((English ("X does not believe in a higher power")) logically implies (English ("X does not believe in God"))) is trivial. And that is the definition of a subset A of B: \forall x \in A, x \in B